Get ready to master the formulas for finding volumes of...
Mathematics58 views·Updated Jul 3, 2026·1 pageVolume of Pyramids, Cones, and Spheres Explained
W
Weswes Wes@wesweswes_fvio
1
of 1
Volume of Pyramids, Cones, and Spheres
Ever wonder how much space is inside a pyramid or a ball? Let's break down these volume formulas so you can solve problems easily!
For a rectangular pyramid, the volume equals one-third of the base area times the height: V = ⅓Bh (where B = L×W). If you have a triangular pyramid, the formula is similar, but the base area is calculated differently: V = ⅓Bh (where B = ½b₁b₂).
Cones follow a similar pattern to pyramids. Their volume is one-third of the base area times the height: V = ⅓πr²h. For spheres, the formula is V = ⅘πr³, where r is the radius of the sphere.
💡 Quick Tip: All these formulas include a fraction (⅓ or ⅘) multiplied by the base area or the cube of the radius. Remember that the base area changes depending on the shape!
Let's look at an example: For a triangular pyramid with a base of 9ft by 12ft and height of 10ft, we calculate: V = ⅓(½×9×12)×10 = ⅓(54)×10 = 180ft³
When solving these problems, take it one step at a time - first find the base area, then multiply by height, and finally multiply by the fraction in the formula.
We thought you’d never ask...
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar Content
Most popular content in Mathematics
9M
MathematicsMath Made Easy: Essential Concepts for Grade 7
Master key math concepts with this comprehensive flashcard set designed specifically for 7th graders. Boost your understanding and ace your exams!
7th7521
G
GeometryGeometry Flashcards: Triangles, Proofs, Angles, and Lines
Master the fundamentals of geometry with these flashcards covering triangles, proofs, angles, and parallel lines. Test your knowledge and ace your exams!
9th3220
M
GeometryMath Flashcards: Triangles, Angles, and Congruent Triangles
Master the fundamentals of geometry with these math flashcards covering triangle angles, parallel lines, and congruent triangles. Test your knowledge and ace your exams!
10th2590
C
MathematicsChapter 2 Quiz. Algebra 1
Equations with variables on both side, literal equations, ratios, conversions, proportions
9th4822
G
GeometryGeometry Essentials
Master the fundamentals of geometry with these flashcards covering angles, triangles, congruent triangles, parallel lines, and polygons.
10th3580
M
Mathematicsmath
learn some new math
6th4233
S
MathematicsSolving X on both sides of an equation
Solve for x when there is x on both sides of equation.
9th2811
M
MathematicsMastering Medium Math: Grade 8 Flashcards
Boost your math skills with these engaging flashcards designed for 8th graders. Ace your exams and become a math whiz!
8th5390
P
MathematicsPEMDAS
PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) Order of operation to solve math problems.
6th3960
Most popular content
9O
AP US HistoryOrigins and Dynamics of the Columbian Exchange
Analyze the ecological and economic motivations behind the initial transfer of goods, people, and diseases between the Old and New Worlds.
9th3,1280
I
AP US HistoryIntroduction to Early Cultural Interactions
Analyze the initial social and religious encounters between Europeans, Africans, and Indigenous peoples in the colonial Americas.
9th2,7730
O
AP World HistoryOrigins of Ancient River Civilizations
Analyze the environmental factors and technological innovations that led to the rise of early states in Mesopotamia, Egypt, and the Indus Valley.
9th3,1870
M
AP US HistoryMotivations for European Exploration
Analyze the economic, religious, and political factors that drove European powers to the Americas during the 15th and 16th centuries.
9th1,7780
F
AP PsychologyFoundations of Ethical Guidelines in Research
Practice the core principles of the APA ethical code including informed consent, debriefing, and the role of Institutional Review Boards.
9th1,3360
I
AP US HistoryIntroduction to Native American Societies
Examine the diverse social, political, and economic structures of North American indigenous groups prior to European contact.
9th1,1100
I
AP US HistoryIntroduction to the Spanish Encomienda System
Explore the fundamental economic and social structures of the Spanish colonial system, focusing on the encomienda and the casta social hierarchy.
9th8890
I
AP BiologyIntroduction to Biological Elements of Life
Practice identifying the essential elements including carbon, nitrogen, phosphorus, and sulfur that compose biological macromolecules.
9th1,7410
O
AP US Government & PoliticsOrigins of the Articles of Confederation
Practice identifying the motivations for a weak central government and the specific powers granted to the states under the first U.S. constitution.
9th9370
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user
Mathematics58 views·Updated Jul 3, 2026·1 pageVolume of Pyramids, Cones, and Spheres Explained
W
Weswes Wes@wesweswes_fvio
Get ready to master the formulas for finding volumes of 3D shapes! In this guide, we'll explore how to calculate the volume of pyramids, cones, and spheres using simple formulas and step-by-step examples.
1
of 1
Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Volume of Pyramids, Cones, and Spheres
Ever wonder how much space is inside a pyramid or a ball? Let's break down these volume formulas so you can solve problems easily!
For a rectangular pyramid, the volume equals one-third of the base area times the height: V = ⅓Bh (where B = L×W). If you have a triangular pyramid, the formula is similar, but the base area is calculated differently: V = ⅓Bh (where B = ½b₁b₂).
Cones follow a similar pattern to pyramids. Their volume is one-third of the base area times the height: V = ⅓πr²h. For spheres, the formula is V = ⅘πr³, where r is the radius of the sphere.
💡 Quick Tip: All these formulas include a fraction (⅓ or ⅘) multiplied by the base area or the cube of the radius. Remember that the base area changes depending on the shape!
Let's look at an example: For a triangular pyramid with a base of 9ft by 12ft and height of 10ft, we calculate: V = ⅓(½×9×12)×10 = ⅓(54)×10 = 180ft³
When solving these problems, take it one step at a time - first find the base area, then multiply by height, and finally multiply by the fraction in the formula.
We thought you’d never ask...
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar Content
Most popular content in Mathematics
9M
MathematicsMath Made Easy: Essential Concepts for Grade 7
Master key math concepts with this comprehensive flashcard set designed specifically for 7th graders. Boost your understanding and ace your exams!
7th7521
G
GeometryGeometry Flashcards: Triangles, Proofs, Angles, and Lines
Master the fundamentals of geometry with these flashcards covering triangles, proofs, angles, and parallel lines. Test your knowledge and ace your exams!
9th3220
M
GeometryMath Flashcards: Triangles, Angles, and Congruent Triangles
Master the fundamentals of geometry with these math flashcards covering triangle angles, parallel lines, and congruent triangles. Test your knowledge and ace your exams!
10th2590
C
MathematicsChapter 2 Quiz. Algebra 1
Equations with variables on both side, literal equations, ratios, conversions, proportions
9th4822
G
GeometryGeometry Essentials
Master the fundamentals of geometry with these flashcards covering angles, triangles, congruent triangles, parallel lines, and polygons.
10th3580
M
Mathematicsmath
learn some new math
6th4233
S
MathematicsSolving X on both sides of an equation
Solve for x when there is x on both sides of equation.
9th2811
M
MathematicsMastering Medium Math: Grade 8 Flashcards
Boost your math skills with these engaging flashcards designed for 8th graders. Ace your exams and become a math whiz!
8th5390
P
MathematicsPEMDAS
PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) Order of operation to solve math problems.
6th3960
Most popular content
9O
AP US HistoryOrigins and Dynamics of the Columbian Exchange
Analyze the ecological and economic motivations behind the initial transfer of goods, people, and diseases between the Old and New Worlds.
9th3,1280
I
AP US HistoryIntroduction to Early Cultural Interactions
Analyze the initial social and religious encounters between Europeans, Africans, and Indigenous peoples in the colonial Americas.
9th2,7730
O
AP World HistoryOrigins of Ancient River Civilizations
Analyze the environmental factors and technological innovations that led to the rise of early states in Mesopotamia, Egypt, and the Indus Valley.
9th3,1870
M
AP US HistoryMotivations for European Exploration
Analyze the economic, religious, and political factors that drove European powers to the Americas during the 15th and 16th centuries.
9th1,7780
F
AP PsychologyFoundations of Ethical Guidelines in Research
Practice the core principles of the APA ethical code including informed consent, debriefing, and the role of Institutional Review Boards.
9th1,3360
I
AP US HistoryIntroduction to Native American Societies
Examine the diverse social, political, and economic structures of North American indigenous groups prior to European contact.
9th1,1100
I
AP US HistoryIntroduction to the Spanish Encomienda System
Explore the fundamental economic and social structures of the Spanish colonial system, focusing on the encomienda and the casta social hierarchy.
9th8890
I
AP BiologyIntroduction to Biological Elements of Life
Practice identifying the essential elements including carbon, nitrogen, phosphorus, and sulfur that compose biological macromolecules.
9th1,7410
O
AP US Government & PoliticsOrigins of the Articles of Confederation
Practice identifying the motivations for a weak central government and the specific powers granted to the states under the first U.S. constitution.
9th9370
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user